Lesson 9: Practical Transformer Model and Calculations

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Lesson 9: Practical Transformer

Model and Calculations

ET 332b Ac Motors, Generators and Power Systems

Lesson 9_et332b.pptx

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Learning Objectives

Lesson 9_et332b.pptx

After this presentation you will be able to:

Identify factors that contribute to non-ideal operation of power transformers

Draw the schematic model of a non-ideal transformer and include all parameters

Reflect impedances through a non-ideal transformer Identify step-up and step down transformer connections Compute transformer voltages and currents using the full

circuit model.

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Lesson 9_et332b.pptx

Transformer Circuit Model

Equivalent Circuit Model for Leakage and Coil Resistance

Leakage Flux

Leakage Flux

Not all developed flux links primary to secondary. Leakage flux only links the turns of the coil that generates it

Leakage flux creates leakage inductance that has leakage reactance. This causes additional voltage drops across the coils

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Lesson 9_et332b.pptx

Leakage Reactance and Voltage Drop

Ep+Elp

Define inductive voltage drop

Vs Vp

Vp Ep Elp

Es-Els

Vs Es Els

Where: Vp = net voltage induced in primary Ep = voltage induced due to mutual flux Elp = voltage induced in primary due to leakage Vs = net voltage induced in secondary Es = voltage induced due to mutual flux Els = voltage induced in the secondary due to leakage

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Lesson 9_et332b.pptx

Coil Resistance and Total Voltage Drop

Resistance of windings modeled by lumped resistance

Primary coil resistance

Secondary coil resistance

Ideal transformer purely turns

ratio

Primary side

Secondary side

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Lesson 9_et332b.pptx

Circuit Model of Non-ideal Transformers

Use ideal transformer impedance formulas to get equivalent Zin Zin is called the reflected or referred impedance

From ideal transformers

Zin

Zin

a2

Vs Is

a2

Np Ns

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Lesson 9_et332b.pptx

Circuit Model of Non-ideal Transformers

From Ohm's Law

Vs Is

(R s

j Xls )

Zload

Zin a 2 (R s j Xls ) a 2 Zload

Zin a 2 R s j a 2 Xls a 2 Zload

Where: a2Rs = secondary R referred to primary a2 Xls = secondary Xls referred to primary a2 Zload = load impedance referred to primary

Referring the secondary impedances to the primary side effectively removes the need for the ideal transformer. The turns ratio captures all the effects

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Lesson 9_et332b.pptx

Circuit Model of Non-ideal Transformers

Transformer circuit with ideal turns ratio removed

Zin Can solve this circuit to find anything about non-ideal transformer operation. Voltage drop, power losses, primary and secondary currents and voltages.

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Simplified Circuit Model

Lesson 9_et332b.pptx

Another simplifying assumption: I0 ................
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